`1 g` mixture of glucose and urea present in `259 mL` aqueous solution shows the osmotic pressure of `0.74 atm` at `27^(@)C`. Assuming solution to be dilute, select the correct statements:

Options

A. Percentage of urea in mixture is `17.6`
B. Relative lowering in vapour pressure of this solution is `5.41 xx 10^(-4)`
C. (c) The solution will boil at `100.015^(@)C`, if `K_(b)` of water is `0.5 K "molality"^(-1)`
D. If glucose is replaced by same amount of sucrose, the solution will show higher osmotic pressure at `27^(@)C`

Answer

A, B, C

Explanation

Let `a` glucose, `b g` urea be present in `1 g`
`:. a+b = 1` ….(1)
Thus, `0.74 xx (250)/(1000) = ((1)/(180)+(b)/(60)) xx 0.0821 xx 300` ….(2)
By eqs. (1) and (2),
`b = 0.176, a = 0.824`
`(P^(@)-P_(S))/(P^(@)) = (w xx M xx 1000)/(m xx W xx 1000)`
`:.` Molality `= (P^(@)-P_(S))/(P^(@)) xx (1000)/(M)`
or `(pi)/(ST) = (P^(@)-P_(S))/(P^(@)) xx (1000)/(M) , (because M = m)`
`:. (P^(@) -P_(S))/(P^(@)) = (0.74 xx 18)/(0.0821 xx 300 xx 1000)`
`= 5.41 xx 10^(-4)`
`Delta T_(b) = "molality" xx K_(b) = (pi)/(ST) xx K_(b)`
`= (0.74)/(0.0821 xx 300) xx 0.5 = 0.015`
`b.pt. = 100.015^(@)C`
On replacing glucose `(mol. wt. 180)` by sucrose (mol wt. 342), `pi` will decreases
as `pi prop (1)/(mol.wt)`
On replacing glucose `(mol. wt. 180)` by `NaCl (mol. wt. 58.5), pi` will increases as
`pi prop (1)/(mol. wt.) xx 2` for `NaCl`